Interest+2C-1

==        == ==       <span style="color: rgb(5, 189, 131)"><span style="color: rgb(5, 189, 131)"><span style="color: rgb(111, 251, 213)"> **__What is interest and when is it used?__**        == toc Interest deals normally with money. It is a percentage of the amount you have or pay that gets added on to the original amount to give you a new total. It is used most often in banking with loans and savings accounts.

__**Types of interest:**__
**Simple interest** is when your total //increases steadily by the same amount (ie. Arithmetic sequences).//

Example #1: if you put $100 into a savings account that has simple interest of 10% a year, after each year you would get 10% of your initial value each year.
 * = Year ||= Amount of money, in dollars ||= Explanation ||
 * 0 || 100.00 || Initial value that you put in ||
 * 1 || 110.00 || 100 + 10 (10% of 100) ||
 * 2 || 120.00 || 100 + 10 + 10 ||
 * 3 || 130.00 || 100 + 10 + 10 + 10 ||

**Compound interest** is when your total //increases by an uneven amount (ie.Geometric sequences)//. In simple interest the interest is taken from the initial value every time. In compound interest the interest is taken from the accumulated amount.

Example #2 : $100 in a savings account with interest of 10% a year. After each year you would get 10% of the money you had in the account from the previous year.


 * = Year ||= Amount of money, in dollars ||||= Explanation ||
 * = 0 ||= 100.00 ||= Initial value that you put in ||
 * = 1 ||= 110.00 ||= 100 + 10 (10% of 100) ||
 * = 2 ||= 121.00 ||= 110 + 11 (10% of 110) ||
 * = 3 ||= 133.10 ||= 121 + 12.10 (10% of 121) ||

Note: Compound interest can also be calculated quarterly or monthly.

Example #3 : $100 in a savings account BUT this time 10% interest is compounded quarterly. Therefore you have to divide 10% by 4, giving you 2.5%. You than use the 2.5% to calculate the interest.
 * = Quarter ||= Year ||= Amount of money, in dollars ||||= Explanation ||
 * = 1 ||=  ||= 100.00 ||= Initial value ||
 * = 2 ||=  ||= 102.50 ||= 100 + 2.5 (2.5% of 100) ||
 * = 3 ||=  ||= 107.69 ||= 102.50 + (2.5% of 102.50) ||
 * = 4 ||= 1 ||= 110.38 ||= 110.38 + (2.5% of 110.38) ||
 * = 5 ||=  ||= 113.14 ||= 113.14 + (2.5% of 113.14) ||
 * = 6 ||=  ||= 115.97 ||= 115.97 + (.025 * 115.97) ||
 * = 7 ||=  ||= 118.87 ||= 118.87 + (.025 * 118.87) ||
 * = 8 ||= 2 ||= 121.84 ||= 121.84 + (.025 * 121.84) ||

__Formulas__
Turning a percentage into a decimal: move the decimal two places to the left. 10.00% → .1 2.00% → .02 5% → .05
 * How do you do the math?**

y = mx + b Where m is the amount being added to you account each year (Initial-value* Percent-interest) x is the year, b is the initial value. Example A: $100 in an account with 10% interest for 4 years → y= 10(4) + 100 → 40 + 100 = $140
 * To calculate Simple interest:** you use the equation


 * To calculate Compound interest:** use the equation

math y= km^x math Where, k is the Initial value m is (1+Percent-interest) x is the number-of-times-interest-calculated

Example B: (compounded yearly): $100 in an account with 10% interest for 4 years math y=100(1+.1)^4 math math =100(1.4641) = $146.41 math

__Powerpoint__
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__Further Discussion__

 * How were these formulas derived?